Her peccadillo aroused a Greek know-it-all (7,6)

I believe the answer is:

delphic oracle

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'a greek know-it-all' is the definition.
I don't know anything about this answer so I cannot judge whether this works.

'her peccadillo aroused' is the wordplay.
'aroused' indicates anagramming the letters (letters roused or stirred up into a new form).
'her'+'peccadillo'='herpeccadillo'
'herpeccadillo' with letters rearranged gives 'DELPHIC ORACLE'.

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